MAP Prior

for (res in list(res1, res3, res5)){
  cat("probability of claiming efficacy is", res$prob_rej, "\n",
    "effective historical sample size is", formatC(res$EHSS, digits = 2, format = "f"), "\n",
    "Mean Width of Credible Interval for Control Prior", formatC(res$width_quantile_interval_mean, digits = 4, format = "f"), "\n",
    "% of times muc is in quantile interval is", formatC(res$quantile_interval_count_mean*100, digits = 4, format = "f"), "\n",
    "Bias of point estiamtor based on control prior", formatC(res$bias_point_est, digits = 4, format = "f"), "\n",
    "Variance value of point estiamtor based on control prior", formatC(res$var_point_est, digits = 4, format = "f"), "\n",
    "MSE of point estiamtor based on control prior", formatC(res$mse_point_est, digits = 4, format = "f"),  "\n", 
    "total time for", 100, "simulations is", formatC(res$time_diff, digits = 4, format = "f"), "\n",
    "power:", formatC(res$power, digits = 4, format = "f"))
  print(res$plot_density)
  print(res$plot_comp)
}
## probability of claiming efficacy is 0 
##  effective historical sample size is 73.04 
##  Mean Width of Credible Interval for Control Prior 0.5006 
##  % of times muc is in quantile interval is 100.0000 
##  Bias of point estiamtor based on control prior -0.0054 
##  Variance value of point estiamtor based on control prior 0.0044 
##  MSE of point estiamtor based on control prior 0.0044 
##  total time for 100 simulations is 0.7360 
##  power: 0.8800

## probability of claiming efficacy is 0 
##  effective historical sample size is 73.04 
##  Mean Width of Credible Interval for Control Prior 0.5008 
##  % of times muc is in quantile interval is 97.0000 
##  Bias of point estiamtor based on control prior 0.1280 
##  Variance value of point estiamtor based on control prior 0.0044 
##  MSE of point estiamtor based on control prior 0.0208 
##  total time for 100 simulations is 0.6228 
##  power: 0.6700

## probability of claiming efficacy is 0 
##  effective historical sample size is 73.04 
##  Mean Width of Credible Interval for Control Prior 0.5081 
##  % of times muc is in quantile interval is 15.0000 
##  Bias of point estiamtor based on control prior 0.3280 
##  Variance value of point estiamtor based on control prior 0.0044 
##  MSE of point estiamtor based on control prior 0.1119 
##  total time for 100 simulations is 0.5466 
##  power: 0.1900

Power Prior

for (res in list(res1, res3, res5)){
  cat("probability of claiming efficacy is", res$prob_rej, "\n",
    "effective historical sample size is", formatC(res$EHSS, digits = 2, format = "f"), "\n",
    "Mean Width of Credible Interval for Control Prior", formatC(res$width_quantile_interval_mean, digits = 4, format = "f"), "\n",
    "% of times muc is in quantile interval is", formatC(res$quantile_interval_count_mean*100, digits = 4, format = "f"), "\n",
    "Bias of point estiamtor based on control prior", formatC(res$bias_point_est, digits = 4, format = "f"), "\n",
    "Variance value of point estiamtor based on control prior", formatC(res$var_point_est, digits = 4, format = "f"), "\n",
    "MSE of point estiamtor based on control prior", formatC(res$mse_point_est, digits = 4, format = "f"),  "\n", 
    "total time for", 100, "simulations is", formatC(res$time_diff, digits = 4, format = "f"), "\n",
    "power:", formatC(res$power, digits = 4, format = "f"))
  print(res$plot_density)
  print(res$plot_comp)
}
## probability of claiming efficacy is 0 
##  effective historical sample size is 68.08 
##  Mean Width of Credible Interval for Control Prior 0.5163 
##  % of times muc is in quantile interval is 100.0000 
##  Bias of point estiamtor based on control prior -0.0026 
##  Variance value of point estiamtor based on control prior 0.0050 
##  MSE of point estiamtor based on control prior 0.0050 
##  total time for 100 simulations is 5.1372 
##  power: 0.8700

## probability of claiming efficacy is 0 
##  effective historical sample size is 67.93 
##  Mean Width of Credible Interval for Control Prior 0.5165 
##  % of times muc is in quantile interval is 97.0000 
##  Bias of point estiamtor based on control prior 0.1261 
##  Variance value of point estiamtor based on control prior 0.0051 
##  MSE of point estiamtor based on control prior 0.0210 
##  total time for 100 simulations is 5.0992 
##  power: 0.6700

## probability of claiming efficacy is 0 
##  effective historical sample size is 67.97 
##  Mean Width of Credible Interval for Control Prior 0.5245 
##  % of times muc is in quantile interval is 21.0000 
##  Bias of point estiamtor based on control prior 0.3189 
##  Variance value of point estiamtor based on control prior 0.0050 
##  MSE of point estiamtor based on control prior 0.1067 
##  total time for 100 simulations is 5.1151 
##  power: 0.1900

Normalized Power Prior

for (res in list(res1, res3, res5)){
  cat("probability of claiming efficacy is", res$prob_rej, "\n",
    "effective historical sample size is", formatC(res$EHSS, digits = 2, format = "f"), "\n",
    "Mean Width of Credible Interval for Control Prior", formatC(res$width_quantile_interval_mean, digits = 4, format = "f"), "\n",
    "% of times muc is in quantile interval is", formatC(res$quantile_interval_count_mean*100, digits = 4, format = "f"), "\n",
    "Bias of point estiamtor based on control prior", formatC(res$bias_point_est, digits = 4, format = "f"), "\n",
    "Variance value of point estiamtor based on control prior", formatC(res$var_point_est, digits = 4, format = "f"), "\n",
    "MSE of point estiamtor based on control prior", formatC(res$mse_point_est, digits = 4, format = "f"),  "\n", 
    "total time for", 100, "simulations is", formatC(res$time_diff, digits = 4, format = "f"), "\n",
    "power:", formatC(res$power, digits = 4, format = "f"))
  print(res$plot_density)
  print(res$plot_comp)
}
## probability of claiming efficacy is 0.02 
##  effective historical sample size is 29.98 
##  Mean Width of Credible Interval for Control Prior 0.8075 
##  % of times muc is in quantile interval is 96.0000 
##  Bias of point estiamtor based on control prior 0.0522 
##  Variance value of point estiamtor based on control prior 0.0376 
##  MSE of point estiamtor based on control prior 0.0404 
##  total time for 100 simulations is 8.6560 
##  power: 0.6100

## probability of claiming efficacy is 0.02 
##  effective historical sample size is 29.86 
##  Mean Width of Credible Interval for Control Prior 0.8092 
##  % of times muc is in quantile interval is 94.0000 
##  Bias of point estiamtor based on control prior 0.0557 
##  Variance value of point estiamtor based on control prior 0.0379 
##  MSE of point estiamtor based on control prior 0.0410 
##  total time for 100 simulations is 8.6268 
##  power: 0.6100

## probability of claiming efficacy is 0.02 
##  effective historical sample size is 30.50 
##  Mean Width of Credible Interval for Control Prior 0.8111 
##  % of times muc is in quantile interval is 95.0000 
##  Bias of point estiamtor based on control prior 0.0614 
##  Variance value of point estiamtor based on control prior 0.0381 
##  MSE of point estiamtor based on control prior 0.0418 
##  total time for 100 simulations is 8.6096 
##  power: 0.6100

Commensurate Power Prior

for (res in list(res1, res3, res5)){
  cat("probability of claiming efficacy is", res$prob_rej, "\n",
    "effective historical sample size is", formatC(res$EHSS, digits = 2, format = "f"), "\n",
    "Mean Width of Credible Interval for Control Prior", formatC(res$width_quantile_interval_mean, digits = 4, format = "f"), "\n",
    "% of times muc is in quantile interval is", formatC(res$quantile_interval_count_mean*100, digits = 4, format = "f"), "\n",
    "Bias of point estiamtor based on control prior", formatC(res$bias_point_est, digits = 4, format = "f"), "\n",
    "Variance value of point estiamtor based on control prior", formatC(res$var_point_est, digits = 4, format = "f"), "\n",
    "MSE of point estiamtor based on control prior", formatC(res$mse_point_est, digits = 4, format = "f"),  "\n", 
    "total time for", 100, "simulations is", formatC(res$time_diff, digits = 4, format = "f"), "\n",
    "power:", formatC(res$power, digits = 4, format = "f"))
  print(res$plot_density)
  print(res$plot_comp)
}
## probability of claiming efficacy is 0.02 
##  effective historical sample size is 29.44 
##  Mean Width of Credible Interval for Control Prior 0.8085 
##  % of times muc is in quantile interval is 96.0000 
##  Bias of point estiamtor based on control prior 0.0590 
##  Variance value of point estiamtor based on control prior 0.0391 
##  MSE of point estiamtor based on control prior 0.0426 
##  total time for 100 simulations is 9.9481 
##  power: 0.6100

## probability of claiming efficacy is 0.02 
##  effective historical sample size is 29.44 
##  Mean Width of Credible Interval for Control Prior 0.8118 
##  % of times muc is in quantile interval is 94.0000 
##  Bias of point estiamtor based on control prior 0.0618 
##  Variance value of point estiamtor based on control prior 0.0390 
##  MSE of point estiamtor based on control prior 0.0428 
##  total time for 100 simulations is 9.9022 
##  power: 0.6000

## probability of claiming efficacy is 0.02 
##  effective historical sample size is 30.15 
##  Mean Width of Credible Interval for Control Prior 0.8154 
##  % of times muc is in quantile interval is 96.0000 
##  Bias of point estiamtor based on control prior 0.0624 
##  Variance value of point estiamtor based on control prior 0.0397 
##  MSE of point estiamtor based on control prior 0.0436 
##  total time for 100 simulations is 9.9895 
##  power: 0.5900

Elastic Prior

for (res in list(res1, res3, res5)){
  cat("probability of claiming efficacy is", res$prob_rej, "\n",
    "effective historical sample size is", formatC(res$EHSS, digits = 2, format = "f"), "\n",
    "Mean Width of Credible Interval for Control Prior", formatC(res$width_quantile_interval_mean, digits = 4, format = "f"), "\n",
    "% of times muc is in quantile interval is", formatC(res$quantile_interval_count_mean*100, digits = 4, format = "f"), "\n",
    "Bias of point estiamtor based on control prior", formatC(res$bias_point_est, digits = 4, format = "f"), "\n",
    "Variance value of point estiamtor based on control prior", formatC(res$var_point_est, digits = 4, format = "f"), "\n",
    "MSE of point estiamtor based on control prior", formatC(res$mse_point_est, digits = 4, format = "f"),  "\n", 
    "total time for", 100, "simulations is", formatC(res$time_diff, digits = 4, format = "f"), "\n",
    "power:", formatC(res$power, digits = 4, format = "f"))
  print(res$plot_density)
  print(res$plot_comp)
}
## probability of claiming efficacy is 0.02 
##  effective historical sample size is 48.51 
##  Mean Width of Credible Interval for Control Prior 0.4970 
##  % of times muc is in quantile interval is 97.0000 
##  Bias of point estiamtor based on control prior 0.0122 
##  Variance value of point estiamtor based on control prior 0.0141 
##  MSE of point estiamtor based on control prior 0.0142 
##  total time for 100 simulations is 34.4223 
##  power: 0.8300

## probability of claiming efficacy is 0.02 
##  effective historical sample size is 47.53 
##  Mean Width of Credible Interval for Control Prior 0.5003 
##  % of times muc is in quantile interval is 92.0000 
##  Bias of point estiamtor based on control prior 0.1043 
##  Variance value of point estiamtor based on control prior 0.0162 
##  MSE of point estiamtor based on control prior 0.0270 
##  total time for 100 simulations is 34.2883 
##  power: 0.6900

## probability of claiming efficacy is 0.02 
##  effective historical sample size is 29.17 
##  Mean Width of Credible Interval for Control Prior 0.6114 
##  % of times muc is in quantile interval is 43.0000 
##  Bias of point estiamtor based on control prior 0.1560 
##  Variance value of point estiamtor based on control prior 0.0605 
##  MSE of point estiamtor based on control prior 0.0848 
##  total time for 100 simulations is 34.1144 
##  power: 0.4800